How do you find the amplitude, period and phase shift for y=1/2sin(theta-pi/2)+4?

1 Answer
Jun 4, 2017

amplitude: 1/2
period:
phase shift: shift right π/2

Explanation:

First start with the base equation of y=asin(bx-c) to find everything, where a=1/2, b=1, and c=π/2.

To find amplitude, the equation is the absolute value of a, or |a|, meaning that the amplitude is 1/2.

To find the period, use the equation (2π)/b. Plug 1 into b to get (2π)/1, so the period is just .

Finally, for the phase shift, use bx+c=0. Plug everything in so that 1Θ-(π/2)=0. Add π/2 to both sides to get Θ=π/2. This shows that the graph will be shifted π/2 units to the right, since it is positive.